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Last updated on April 28th, 2025
A number we multiply by itself three times to get the original number is its cube root. It has various uses in real life, such as finding the volume of cube-shaped objects and designing structures. We will now find the cube root of 106480 and explain the methods used.
We have learned the definition of the cube root. Now, let’s learn how it is represented using a symbol and exponent. The symbol we use to express the cube root is the radical sign (∛), and the exponent we use is ⅓.
In exponential form, ∛106480 is written as (1064801/3). The cube root is just the opposite operation of finding the cube of a number. For example, assume ‘y’ as the cube root of 106480, then \(y^3\) can be 106480. The cube root of 106480 is not an exact integer, but it can be written as approximately 47.512.
Finding the cube root of a number is to identify the number that must be multiplied by itself three times to result in the target number. Now, we will go through the different ways to find the cube root of 106480. The common methods we follow to find the cube root are given below:
To find the cube root of a non-perfect number, we often follow Halley’s method. Since 106480 is not a perfect cube, we use Halley’s method.
Let's find the cube root of 106480 using Halley’s method.
The formula is ∛a ≅ x(frac{(x3 + 2a)}{(2x3 + a)})
where: a = the number for which the cube root is being calculated
x = the nearest perfect cube
Substituting, a = 106480;
x = 47
∛a ≅ 47(frac{(473 + 2 × 106480)}{(2 × 473 + 106480)})
∛106480 ≅ 47.512
The cube root of 106480 is approximately 47.512.
Imagine you have a cube-shaped container that has a total volume of 106480 cubic centimeters. Find the length of one side of the container equal to its cube root.
A construction project requires 106480 cubic meters of material. Calculate the amount of material left after using 1000 cubic meters.
A tank holds 106480 cubic meters of water. Another tank holds a volume of 2000 cubic meters. What would be the total volume if the tanks are combined?
When the cube root of 106480 is multiplied by 2, calculate the resultant value. How will this affect the cube of the new value?
Find ∛(53000 + 53480).
Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.
: He loves to play the quiz with kids through algebra to make kids love it.